Method and apparatus for detecting edge of image and computer readable medium processing method

ABSTRACT

The present invention provides a method and apparatus for detecting a noise distribution of an image close to a true distribution, and detecting an edge of the image precisely and quickly based on the detected noise distribution without performing a smoothing process for the image, and a computer readable medium processing the method. The method of detecting an edge of an image includes the steps of: detecting a noise distribution of an object image; and detecting an edge of the image based on the detected noise distribution.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and apparatus for detecting anedge of an object image and a computer readable medium processing themethod.

2. Description of the Related Art

A Conventional

In general, a conventional apparatus for detecting an edge of an objectperforms a smoothing process for an image taken by a camera in order toreduce noises present in the image. In this case, a structure of thesmoothed image is varied. That is, position of an edge line of thesmoothed image becomes different from position of an actual edge line,especially around a corner. In addition, the conventional image edgedetecting apparatus may remove minute variation (minute edge) of theimage as well as the noises according to parameters.

The conventional image edge detecting apparatus divides a degree of edgeof the image according to values set by a user. For example, theconventional image edge detecting apparatus detects the edge of theimage according to image brightness, scene and camera set by the user.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide amethod and apparatus for detecting a noise distribution of an imageclose to a true distribution, and detecting an edge of the imageprecisely and quickly based on the detected noise distribution withoutperforming a smoothing process for the image, and a computer readablemedium processing the method.

To achieve the above object, according to an aspect of the invention,there is provided a method of detecting an edge of an image, includingthe steps of: detecting a noise distribution of an object image; anddetecting an edge of the image based on the detected noise distribution.

According to another aspect of the invention, there is provided anapparatus for detecting an edge of an image, including: a noisedetecting unit that detects a noise distribution of an object image; andan edge detecting unit that detects an edge of the image based on thedetected noise distribution.

According to still another aspect of the invention, there is provided acomputer readable medium recorded with a program for performing theabove method.

The medium includes all kinds of record media in which programs and dataare stored so that they can be read by a computer system. For example,the medium may include a ROM (Read Only Memory), a RAM (Random AccessMemory), a CD (Compact Disk), a DVD (Digital Video Disk)-ROM, a magnetictape, a floppy disk, an optical data storage, etc., and may beimplemented with the form of carrier waves (for example, transmissionthrough the Internet). In addition, the medium may be distributed incomputer systems interconnected by a network so that computer readablecodes can be stored and executed in a distributed processing system.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects and advantages of the present inventionwill become apparent and more readily appreciated from the followingdescription of the embodiments, taken in conjunction with theaccompanying drawings of which:

FIG. 1 is a view showing a configuration of an image edge detectingapparatus according to an embodiment of the present invention;

FIGS. 2 a and 2 b are views illustrating concept and result of edgedetection for explaining an image edge detecting method and apparatusaccording to an embodiment of the present invention;

FIG. 3 is a view showing an example of a probability mass function of aSkellam distribution;

FIGS. 4 a to 4 d are views showing Skellam and Gaussian distributionsdepending on μ₁ and μ₁;

FIGS. 5 a to 5 c are views showing Skellam parameter estimation resultsusing static images;

FIGS. 6 a to 6 d are views showing comparison between modeling resultsin spatial and temporal domains;

FIGS. 7 a to 7 c are views showing linearity between a sample mean of apatch and a Skellam parameter;

FIG. 8 is a view showing a histogram of intensity in an R channel anddetected local maxima;

FIGS. 9 a to 9 c are views showing estimation results of anIntensity-Skellam line of each channel in two static images;

FIGS. 10 a and 10 b are views showing variation of a Skellam parameterat an edge line;

FIGS. 11 a and 11 b are views showing a histogram for a differencebetween Skellam parameters;

FIGS. 12 a to 12 c are views showing estimation results of imageintensity and a Skellam line in a single image;

FIG. 13 is a view showing intensity allowance of a given probabilitydensity function;

FIGS. 14 a to 14 f are a first exemplary view showing comparison betweenan edge detection result according to an embodiment of the presentinvention and an edge detection result of a Canny edge detector;

FIGS. 15 a to 15 f are a second exemplary view showing comparisonbetween an edge detection result according to an embodiment of thepresent invention and an edge detection result of a Canny edge detector;and

FIGS. 16 a to 16 d are views showing edge detection results depending onvarious illumination changes.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Hereinafter, preferred embodiments of a method and apparatus fordetecting a noise distribution of an image without performing asmoothing process for the image, and detecting an edge of the imageprecisely and quickly based on the detected noise distribution will bedescribed in detail with reference to the accompanying drawings.

FIG. 1 is a view showing a configuration of an image edge detectingapparatus 10 according to an embodiment of the present invention.

Referring to FIG. 1, the image edge detecting apparatus 10 according tothe embodiment of the present invention includes a noise detecting unit11 that detects a noise distribution in an object image, and an edgedetecting unit 12 that detects an edge (or boundary) of the image basedon the detected noise distribution. Here, the image edge detectingmethod and apparatus can be applied to a chare-coupled device (CCD)camera.

The noise detecting unit 11 estimates the noise distribution accordingto a linear relationship between noise parameters of the image andintensity of the image and outputs the estimated noise distribution tothe edge detecting unit 12.

The edge detecting unit 12 detects the edge of the image based on theestimated noise distribution and outputs the detected edge to a displayunit 20. At this time, the display unit 20 displays an edge image of theoriginal image on a screen.

Hereinafter, concept and result of edge detection of an object imagetaken with the CCD camera will be described with reference to FIGS. 2 aand 2 b.

FIGS. 2 a and 2 b are views illustrating concept and result of edgedetection for explaining an image edge detecting method and apparatusaccording to an embodiment of the present invention. That is, FIGS. 2 aand 2 b show general concept and result of edge detection of an image.

As shown in FIGS. 2 a and 2 b, a noise distribution for each intensitycan be determined through linearity between Skellam parameters and asample mean of a patch, that is intensity, and intensity allowance canbe determined based on the determined noise distribution. For example,when the noise distribution depending on intensity at each pixel isdetermined, it can be determined whether a difference between pixelsderives from noise or change of an actual scene based on the determinedintensity allowance.

Hereinafter, a Skellam distribution for noise modeling of an intensitydifference will be described.

First, assuming that image intensity of each pixel obeys a Poissondistribution, a probability distribution for photon p for an observationtime interval T becomes a Poisson distribution according to Equation 1.

$\begin{matrix}{{P\left( {\left. p \middle| \rho \right.,T} \right)} = \frac{\left( {\rho\; T} \right)^{p}{\mathbb{e}}^{{- \rho}\; T}}{p!}} & \left\lbrack {{Equation}\mspace{20mu} 1} \right\rbrack\end{matrix}$

Here, ρ is a ratio of measured photon per second. The mean μ and thestandard deviation σ are given as Equations 2 and 3μ=ρT  [Equation 2]σ=√{square root over (ρT)}  [Equation 3]

Since the number of photons determines the intensity of pixel. Photonnoise is not independent of a signal. In addition, the photon noise isneither Gaussian nor additional. In Equations 2 and 3, μ means thenumber of photons for the interval T. It is natural that the number ofphotons in a bright pixel should be larger than the number of photons ina dark pixel. From this fact, it can be expected that μ increases withincrease of intensity. This expectation will be proved as follows.

If μ is sufficiently large, the Poisson distribution can be approximatedto a Gaussian distribution. Then, since a difference between twoGaussians obeys Gaussian, a distribution of an intensity difference willalso be Gaussian. However, μ is varied depending on intensity. Thismeans that a Gaussian approximation may be broken.

The Poisson distribution is directly used to represent the intensitydifference in order to avoid a wrong Gaussian approximation. Adifference between two Poisson probability parameters is defined by aSkellam distribution. A probability mass function of the Skellamdistribution is a function of k that means the difference between twoPoisson probability parameters and is expressed as Equation 4.

$\begin{matrix}{{f\left( {{k;\mu_{1}},\mu_{2}} \right)} = {{{\mathbb{e}}^{- {({\mu_{1} + \mu_{2}})}}\left( \frac{\mu_{1}}{\mu_{2}} \right)}^{k/2}{I_{k}\left( {2\sqrt{\mu_{1}\mu_{2}}} \right)}}} & \left\lbrack {{Equation}\mspace{20mu} 4} \right\rbrack\end{matrix}$

Here, each of μ₁ and μ₂ refers to the mean or an expected value, andI_(k) refers to a modified Bessel function of the first kind.

Hereinafter, an example of the probability mass function of the Skellamdistribution will be described with reference to FIG. 3.

FIG. 3 is a view showing an example of the probability mass function ofthe Skellam distribution.

First, in a special case of μ₁=μ₂, the Skellam distribution for μ and khaving a large value tends to become a Gaussian distribution. Since μand k do not have a sufficiently large value for a pixel having lowintensity, the Skellam distribution can not be approximated as theGaussian distribution. This fact will be described with reference toFIGS. 4 a to 4 d.

FIGS. 4 a to 4 d are views showing the Skellam and Gaussiandistributions depending on μ₁ and μ₂.

FIG. 4 a shows the Skellam and Gaussian distributions when μ₁=μ₂=0.1 andσ=0.2, FIG. 4 b shows the Skellam and Gaussian distributions whenμ₁=μ₂=0.5 and σ=1.0, FIG. 4 c shows the Skellam and Gaussiandistributions when μ₁μ₂=1.0 and σ=2.0, and FIG. 4 d shows the Skellamand Gaussian distributions when μ₁=μ₂=3.0 and σ=6.0.

Accordingly, Skellam parameters of intensity difference can be easilyestimated using statistics of the Skellam distribution. Mean μ_(s) andvariance σ_(s) ² are given as Equations 5 and 6.μ_(s)=μ₁−μ₂  [Equation 5]σ_(s) ²=μ₁+μ₂  [Equation 6]

Here, according to Equations 5 and 6, μ₁ and μ₂ can be directly obtainedaccording to Equations 7 and 8.

$\begin{matrix}{\mu_{1} = \frac{\mu_{S} + \sigma_{S}^{2}}{2}} & \left\lbrack {{Equation}\mspace{20mu} 7} \right\rbrack \\{\mu_{2} = \frac{\mu_{S} - \sigma_{S}^{2}}{2}} & \left\lbrack {{Equation}\mspace{20mu} 8} \right\rbrack\end{matrix}$

Here, μ_(s) and variance σ_(s) ² can be obtained from an image of astatic scene according to Equations 9 and 10.

$\begin{matrix}{\mu_{S} = \frac{\sum\limits_{t}\left( {{x_{t}\left( {i,j} \right)} - {x_{t + 1}\left( {i,j} \right)}} \right)}{n}} & \left\lbrack {{Equaiton}\mspace{20mu} 9} \right\rbrack \\{\sigma_{S}^{2} = \frac{\sum\limits_{t}\left( {\mu_{S} - \left( {{x_{t}\left( {i,j} \right)} - {x_{t + 1}\left( {i,j} \right)}} \right)} \right)^{2}}{n}} & \left\lbrack {{Equation}\mspace{20mu} 10} \right\rbrack\end{matrix}$

Here, x_(t)(i,j) is intensity of a position (i,j) at a frame t, and n isthe total number of images. In order to estimate the Skellam parametersin a variety of colors, 10,000 images are acquired for a static scene of“Gretag-Macbeth ColorChecker.” A camera used is “Pointgrey Scorpion.” Atthis time, estimation results (image resolution: 1600×1200, and exposuretime: 1/15 second) are as shown in FIGS. 5 a to 5 c.

FIG. 5 a to 5 c are views showing Skellam parameter estimation resultsusing 10,000 static images. FIG. 5 a shows a Skellam parameterestimation result for a black patch (24th patch), FIG. 5 b shows aSkellam parameter estimation result for a gray patch (21st patch), andFIG. 5 c shows a Skellam parameter estimation result for a red patch(15th patch).

That is, the Skellam parameters are different for different patches. Theblack patch has a low Skellam parameter and the gray patch has a highSkellam parameter. This is expected from the fact that μ₁ and μ₂ are thenumber of photons obtained for acquisition time in the CCD device.

In addition, FIGS. 5 a to 5 c show different important verification.That is, a distribution of intensity difference can be preciselyestimated from a Skellam modeling. This shows that the photon noiseassumed in the present invention is appropriately dominant.

As shown in FIGS. 5 a to 5 c, noise has to be estimated from a singleimage in order to generalize the Skellam modeling. In the presentinvention, it is assumed that pixels are independent of each other in aspatial domain. This means that a noise distribution in the spatialdomain is equal to that in a temporal domain. In order to prove thatthis assumption is proper, the noise distribution in the spatial domainis compared with that in the temporal domain. A modeling result in thetemporal domain can be obtained according to Equations 9 and 10.Monochromatic color patches are cut out of a color pattern image inorder to model noise in the spatial domain. The noise modeling in thespatial domain can be obtained using the cut patches according toEquations 11 and 12.

$\begin{matrix}{\mu_{S} = \frac{\sum\limits_{{({i,j})} \in P}\left( {{x_{t}\left( {i,j} \right)} - {x_{t}\left( {{i + d_{x}},{j + d_{y}}} \right)}} \right)}{n}} & \left\lbrack {{Equation}\mspace{20mu} 11} \right\rbrack \\{\sigma_{S}^{2} = \frac{\sum\limits_{{({i,j})} \in P}\left( {\mu_{S} - \left( {{x_{t}\left( {i,j} \right)} - {x_{t}\left( {{i + d_{x}},{j + d_{y}}} \right)}} \right)} \right)^{2}}{n}} & \left\lbrack {{Equation}\mspace{20mu} 12} \right\rbrack\end{matrix}$

Here, (i,j)εP means all point in the patches, and d_(x) and d_(y) meandisparity in horizontal and vertical directions, respectively. n is thetotal number of pixels in the patches.

Hereinafter, comparison between modeling results in the spatial andtemporal domains will be described with reference to FIGS. 6 a to 6 d.

FIGS. 6 a to 6 d are views showing comparison between modeling resultsin the spatial and temporal domains.

FIG. 6 a shows comparison between modeling results in the spatial andtemporal domains for an orange patch (7th patch), FIG. 6 b showscomparison between modeling results in the spatial and temporal domainsfor a blue patch (13th patch), FIG. 6 c shows comparison betweenmodeling results in the spatial and temporal domains for a green patch(14th patch), and FIG. 6 d shows comparison between modeling results inthe spatial and temporal domains for a medium gray patch (22nd patch).Here, a camera used for the modeling in the spatial and temporal domainsis “Pointgrey Scorpion.” At this time, estimation results (imageresolution: 1600×1200, and exposure time: 1/7.5 second) As shown inFIGS. 6 a to 6 d, it can be proved that the Skellam parameters in thetemporal and spatial domains are nearly equal to each other. This showsthat intensity difference is ergodic. If disparity is 1, it can be saidthat a Skellam parameter is smaller than different estimation results.This seems to occur from compression of pixel values. In a test using acamera having a non-compression RGB output function such as HITACHIHV-F22, it is confirmed that this phenomenon does not occur. A smalldifference between modeling results in the spatial and temporal domainsoccurs because only one pixel in the patch is selected when the noisedistribution in the temporal domain is estimated. A small variation ofthe Skellam parameters may occur depending on which pixel in the patchis selected. This experiment shows that disparity in the horizontal andvertical directions has the same result although d_(x) increases from 1to 10. Since the suggested modeling system satisfies ergodicity, thissystem can be applied to a single image.

Hereinafter, a method of estimating noise statistics using the Skellamparameters will be described.

First, although the Skellam modeling can be applied to the spatialdomain as well as the temporal domain, linearity between image intensityand the Skellam parameters is used to find precise Skellam parameters.

FIGS. 7 a to 7 c are views showing linearity between the sample mean ofa patch and a Skellam parameter. That is, in the present invention, anoise distribution of an image is estimated based on a linearrelationship between the Skellam parameter and intensity of the image.

FIG. 7 a shows a linearity relationship between a Skellam parameter ofan image for a red (R) channel and image intensity, FIG. 7 b shows alinearity relationship between a Skellam parameter of an image for agreen (G) channel and image intensity, and FIG. 7 c shows a linearityrelationship between a Skellam parameter of an image for a blue (B)channel and image intensity. Here, since it is difficult to extractmeaningful statistics of mean and variance from a single pixel, 10,000pattern images are acquired in order to show a correlation between theimage intensity and the Skellam parameter.

FIGS. 7 a to 7 c show Skellam parameter scatter plots related to asample mean of pixels at positions defined in patches and the linearityrelationship between the sample mean and the Skellam parameter. In thefigures, a line corresponding to the linearity relationship between thesample mean and the Skellam parameter is called an intensity-Skellamline. If a pixel value can be approximated to the sample mean and hasthe intensity-Skellam line, the Skellam parameter can be estimated.Straight lines in FIGS. 7 a to 7 c are varied only depending on anamplitude gain of a camera, not scene and illumination. In addition,once the intensity-Skellam line is determined, these straight lines canbe used as long as the amplitude gain is fixed.

Hereinafter, a method of estimating the intensity-Skellam line in twogiven static images will be described.

First, if the two static images have pairs of Skellam parameters andintensity values, a line matching these pairs can be obtained. IfSkellam parameters of particular pixels in the temporal domain are to beobtained, at least 10,000 static images are required to sufficientlystabilize statistics to be calculated. However, it is unpractical toacquire so many static images in indoor and outdoor environments. Thepresent invention provides an intensity-Skellam line estimating methodwhich is capable of reducing the number of required static images totwo, which is even more practical than the case where 10,000 staticimages are acquired. Assuming that pixels in pixels are independent ofeach other, intensity differences between corresponding pixels in twoimages can be regarded as a set of intensity differences in the temporaldomain. Therefore, the number of pixels used to estimate Skellamparameters at specified intensity is sufficiently large. A lineestimation algorithm for one channel is as follows.

1. A histogram of intensity in a first frame is obtained and localmaxima are found in the histogram. x_(m) ¹,m=0, 1 , . . . , M

2. A set of corresponding pixels of two frames satisfying Equation 13near the local maxima is found.X _(m) ={x ¹(i,j),x ²(i,j)|x _(m) −ε<x ¹(i,j)<x _(m)+ε}  [Equation 13]

3. Mean and variance of a set Skellam distribution for X_(m) arecalculated from Equations 14 and 15.

$\begin{matrix}{\left. \mu_{S} \middle| X_{m} \right. = \frac{\sum\limits_{X_{m}}\left( {{x_{k}^{1}\left( {i,j} \right)} - {x_{k}^{2}\left( {i,j} \right)}} \right)}{n}} & \left\lbrack {{Equation}\mspace{20mu} 14} \right\rbrack \\{\left. \sigma_{S}^{2} \middle| X_{m} \right. = \frac{\sum\limits_{X_{m}}\left( \mu_{S} \middle| {X_{m} - \left( {{x_{k}^{1}\left( {i,j} \right)} - {x_{k}^{2}\left( {i,j} \right)}} \right)} \right)}{n}} & \left\lbrack {{Equation}\mspace{20mu} 15} \right\rbrack\end{matrix}$

4. Skellam parameters, μ₁ and μ₂ are calculated from Equations 7 and 8.

5. Two lines for a pair of (X_(m) ¹,μ₁) and (X_(m) ¹,μ₂) are estimatedusing a general RANSAC (RANdom SAmple Consensus) method.

Two actual color pattern images are acquired and an experiment for theline estimation algorithm is conducted. The acquisition of two colorpattern images is for obtaining intensity-Skellam lines close to actualvalues (ground truth) from a great number of static images and comparingthe obtained intensity-Skellam lines.

Hereinafter, a histogram of intensity in the R channel and detectedlocal maxima will be described with reference to FIG. 8.

FIG. 8 is a view showing the histogram of intensity in the R channel andthe detected local maxima.

As shown in FIG. 8, pair of intensity and Skellam parameters can beobtained from the local maxima. Here, ε is defined to be 1. In addition,an intensity-Skellam line is determined through RANSAC.

Hereinafter, an estimation result of the intensity-Skellam line in thetemporal domain is will be described with reference to FIGS. 9 a to 9 c.

FIGS. 9 a to 9 c are views showing estimation results of anIntensity-Skellam line in each channel.

FIG. 9 a shows an estimation result of an intensity-Skellam line in theR channel, FIG. 9 b shows an estimation result of an intensity-Skellamline in the G channel, and FIG. 9 c shows an estimation result of anintensity-Skellam line in the B channel. Here, Straight lines obtainedfrom 10,000 static images are plotted for comparison between theintensity-Skellam lines. That is, the estimated intensity-Skellam linesshow highly precise results as compared to actual values. Since most ofthe pairs of intensity and Skellam parameters used to obtain theintensity-Skellam lines are near the estimated intensity-Skellam lines,the intensity-Skellam lines can be obtained using a small number ofpairs of intensity and Skellam parameters.

Hereinafter, a method of estimating an intensity-Skellam line in asingle image will be described.

At least two static images are required to estimate theintensity-Skellam line. There are fields using a single image, such asfeature point extraction and image segmentation, in a computer vision.Samples in the spatial domain instead of the temporal domain can becollected based on the ergodic characteristics. If patches having amonochromatic color are to be found, a Skellam parameter correspondingto the sample mean can be calculated.

In addition, in the present invention, proper patches are found usingcharacteristics of Skellam parameters. The Skellam mean is calculated asthe mean of intensity differences of neighborhood pixels, as expressedby Equation 11. If a color changing portion exists among theneighborhood pixels, it causes variation of the Skellam mean, which willbe described with reference to FIGS. 10 and 10 b.

FIGS. 10 a and 10 b are views showing variation of a Skellam parameterat an edge line.

As shown in FIGS. 10 a and 10 b, an experiment with red-black changingpatch is conducted to show variation of the Skellam parameter at theedge line. That is, when a portion of the patch is changed as the patchmoves to the right (on an X position), the Skellam parameter increases.

If an image is acquired under directional illumination conditions, theSkellam mean at the patch may be shifted little by little even when theimage has a monochromatic color. A histogram of the Skellam mean isfirst obtained to consider such shift. The highest point in thehistogram of the Skellam mean is used to consider the shift of theSkellam mean. Although the illumination is located in the upperdirection, the Skellam mean is little shifted on the experiment.

FIGS. 11 a and 11 b are views showing a histogram for a differencebetween Skellam parameters. FIG. 11 b shows a histogram of the Skellammean for an input image of FIG. 11 a.

As shown in FIGS. 11 a and 11 b, the highest point can be easily foundand patches having the Skellam mean near the highest point are used.Pairs of patch intensity and Skellam parameters are not laid on a singlestraight line. In addition, there may exist singular points notfiltered. In the present invention, a simple RANSAC Algorithm is appliedto estimate a straight line. Since lots of patches are distributed onthe center, the straight line can be easily found. Accordingly, patchesare randomly selected to save time. 1000 19×19 patches are used.

FIGS. 12 a to 12 c are views showing estimation results of imageintensity and a Skellam line in a single image. A noise modelingsuggested based on the estimation results can be applied to the singleimage.

Hereinafter, a method of determining intensity allowance will bedescribed.

Since image intensity values have respective Skellam parameters, imageintensity has a precise distribution according to the Skellamparameters. Allowance of intensity variation occurring due to sensornoise can be determined based on this distribution. A method ofdetermining the intensity allowance is to verify a hypothesis for agiven confidence interval.

A cumulative distribution function has to be used to verify thehypothesis. Since the probability mass function of the Skellamdistribution is defined for only an integer, the cumulative distributionfunction can be calculated as Equation 16.

$\begin{matrix}{{F\left( {{K;\mu_{1}},\mu_{2}} \right)} = {\sum\limits_{k = {- \infty}}^{K}{{{\mathbb{e}}^{- {({\mu_{1} + \mu_{2}})}}\left( \frac{\mu_{1}}{\mu_{2}} \right)}^{k/2}{I_{k}\left( {2\sqrt{\mu_{1}\mu_{2}}} \right)}}}} & \left\lbrack {{Equation}\mspace{20mu} 16} \right\rbrack\end{matrix}$

An acceptance region for critical value I is expressed as Equation 17.A(I)={ν|ν<I}=F(I;μ ₁,μ₂)−F(−I;μ ₁,μ₂)   [Equation 17]

Intensity allowance I_(A) is determined according to Equation 18.

$\begin{matrix}{I_{A} = {{\arg\;{\max\limits_{i}{{A(I)}\mspace{14mu}{s.t.\mspace{11mu}{A(I)}}}}} \leq {1 - \alpha}}} & \left\lbrack {{Equation}\mspace{20mu} 18} \right\rbrack\end{matrix}$

Here, α is a size of I type error meaning a true rejection rate to givea confidence interval of (1−α)*100%, as shown in FIG. 13.

FIG. 13 is a view showing intensity allowance of a given probabilitydensity function. Here, 1−α represents the sum of length of solid linesand α represents the sum of length of dashed lines.

Hereinafter, a method of applying the noise modeling to edge detectionwill be described.

First, the suggested noise modeling is applied to edge detection bydirectly using the intensity allowance. Although a general image edgedetecting method and apparatus smoothes an image as a pre-processthrough a Gaussian kernel, the edge detecting method and apparatus basedon the noise modeling according to the embodiment of the presentinvention need not smooth an image since variation of image intensitydue to sensor noises can be precisely known. The edge detecting methodand apparatus based on the noise modeling according to the embodiment ofthe present invention alleviates noises in an image as well as finding adetailed edge instead of Gaussian smoothing.

Hereinafter, a method of detecting an edge in an image and apost-process will be described.

Since the intensity allowance can be precisely determined based on thenoise estimation using the Skellam distribution, an edge in the imagecan be simply detected. That is, the method of detecting the edge in theimage is highly similar to a method of detecting variations in theimage. For example, if an intensity difference between two adjacentpixels falls within the intensity allowance, the edge detecting unit 12of FIG. 1 determines that there is no edge in the image, or otherwise,there are variations of color in a true scene, and the edge detectingunit 12 determines that there is any edge in the image. A degree of edgein the horizontal and vertical directions is defined according toEquations 19 and 20.

$\begin{matrix}{{e_{x}^{c}\left( {i,j} \right)} = \frac{{{{x^{c}\left( {{i - 1},j} \right)} - {x^{c}\left( {{i + 1},j} \right)}}} - I_{A}}{I_{A}}} & \left\lbrack {{Equation}\mspace{20mu} 19} \right\rbrack \\{{e_{y}^{c}\left( {i,j} \right)} = \frac{{{{x^{c}\left( {i,{j - 1}} \right)} - {x^{c}\left( {i,{j + 1}} \right)}}} - I_{A}}{I_{A}}} & \left\lbrack {{Equation}\mspace{20mu} 20} \right\rbrack\end{matrix}$

Here, I_(A) means intensity allowance in a pixel, c means red, green andblue color channels in an RGB color space, and x(i,j) means a pixelvalue at a position (i,j) of an image. The degree of edge is defined bymeasuring a normalized distance of image intensity from the intensityallowance. If degrees of edges are negative in both of the horizontaland vertical directions, a pixel concerned is regarded as a pixel havingno edge, or otherwise, degrees of edges in both of the horizontal andvertical directions are summed. As a result, the total degree of edgesin one pixel is expressed by Equation 21.

$\begin{matrix}{{e\left( {i,j} \right)} = \left\{ \begin{matrix}{0,} & {{if}\mspace{14mu}\left\{ {\begin{matrix}{{e_{x}^{c}\left( {i,j} \right)} < 0} \\{{e_{y}^{c}\left( {i,j} \right)} < 0}\end{matrix}\mspace{11mu}{for}\mspace{14mu}{all}\mspace{14mu} c} \right.} \\{{{\sum\limits_{c}{e_{x}^{c}\left( {i,j} \right)}} + {\sum\limits_{c}{e_{y}^{c}\left( {i,j} \right)}}},} & {otherwise}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{20mu} 21} \right\rbrack\end{matrix}$

The total degree of edges is preveniently reduced to a degree of edgedue to sensor noise.

After the degree of edge is calculated for all pixels, a non-maximumsuppression process is performed since a true edge does not appear as asingle straight line. A Canny edge, which is most frequently used,requires two values for hysteresis classification in order tointerconnect edges after the non-maximum suppression. However, in thepresent invention, since the intensity difference falls outside theintensity allowance determined based on the noise distribution, a degreeof edge which is not zero regards a pixel concerned as an edge pixel.

Hereinafter, an image edge detection result according to an embodimentof the present invention will be described with reference to FIGS. 15 ato 15 f.

FIGS. 14 a to 14 f are a first exemplary view showing comparison betweenan image edge detection result according to an embodiment of the presentinvention and an image edge detection result of a Canny edge detector.An image edge detecting apparatus according to an embodiment of thepresent invention is compared with a Canny edge detector provided inMATLAB. Here, the image edge detecting apparatus according to theembodiment of the present invention has only one parameter of aconfidence interval.

As shown in FIGS. 14 a to 14 f, Canny edge detectors have threeparameters of high and low critical values for scale of Gaussiansmoothing and hysteresis connection, respectively. These critical valuesare very susceptible in some cases and have a great effect onperformance of the apparatus. Three results are given as automatic, highand low critical (or threshold) values with scale of the Gaussiansmoothing fixed. The image edge detecting apparatus of this inventionshows performance superior to that of the three Canny edge detectors.The image edge detecting apparatus of this invention alleviates most ofwrongly detected edges as compared to the results of the low andautomatic critical values in the Canny edge detectors. In addition, theimage edge detecting apparatus of this invention shows details similarto the result of the low critical value. This is possible because pixelsdetermine critical values differently based on the estimated noisedistribution.

FIGS. 15 a to 15 f are a second exemplary view showing comparisonbetween an edge detection result according to an embodiment of thepresent invention and an edge detection result of a Canny edge detector.

FIGS. 15 a to 15 f show edge detection results when scale of Gaussiansmoothing is varied in the Canny edge detector. Canny critical valuesare automatically selected in MATLAB. Position estimation is very wellconserved in the edge detecting apparatus, but in the Canny edgedetector, the position estimation is not properly made by smoothing of ascale so sufficiently high as to alleviate unexpected edges due to imagenoises.

Hereinafter, edge detection results depending on various illuminationchanges will be described with reference to FIGS. 16 a to 16 d.

FIGS. 16 a to 16 d are views showing edge detection results depending onvarious illumination changes.

As shown in FIGS. 16 a to 16 d, edge detection results in the Canny edgedetector and the edge detecting apparatus of this invention show anormalized degree of edge. For a dark input image, the Canny edgedetector can not find a minute edge even if the Canny edge has a lowcritical value, but the edge detecting apparatus of this invention canfind a fine edge. For a bright input image, repeated edges similar toedges in an image of ordinary illumination can be obtained in the edgedetecting apparatus of this invention. However, the Canny edge detectorcan not alleviate wrong alarm occurring in a portion of monochromaticcolor. Accordingly, the image edge detecting method and apparatusaccording to the embodiment of the present invention shows highrepetition performance for various illumination variations.

As apparent from the above description, the present invention providesan image edge detecting method and apparatus which shows excellentperformance in an automated system, as compared to conventional edgedetecting method and apparatuses, and a computer readable mediumprocessing the method. The biggest problem in applying the conventionaledge detecting methods and apparatuses to industrial systems is thatusers have to correct parameters of edge detection according tovariations of scenes or illuminations. However, the edge detectingmethod and apparatus according to the embodiment of the presentinvention show robust results even under such variations, as shown inFIGS. 16 a to 16 d, as compared to the conventional edge detectingmethods and apparatuses. For example, the edge detecting method andapparatus according to the embodiment of the present invention can knowa structure of a scene of an image so dark as not to be perceived bypersons and effectively remove noises even for an image so bright as notto be removed by the conventional edge detecting methods andapparatuses.

In addition, the conventional edge detecting methods and apparatuseshave a problem in that image edges have a curved shape, not an actualsharp straight line shape, according to a level of smoothing. However,since the edge detecting method and apparatus according to theembodiment of the present invention does not require a smoothingprocess, this edge detecting method and apparatus can precisely detectimage edges, and thus, can be effectively used to develop systems fordiscovering a precise structure of a scene of an image.

While the present invention has been particularly shown and describedwith reference to exemplary embodiments thereof, it will be understoodby those skilled in the art that various changes in form and details maybe made therein without departing from the spirit and scope of thepresent invention. The exemplary embodiments are provided for thepurpose of illustrating the invention, not in a limitative sense. Thus,it is intended that the present invention covers the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A method of detecting an edge of an image,comprising the steps of: detecting a noise distribution of an objectimage by estimating the noise distribution according to correlationbetween noise parameters of the image and intensity of the image, thenoise parameters being Skellam parameters detected from pairs of Skellamparameters and intensity of a set of same pixels having the sameintensity of two static images; and detecting an edge of the image basedon the detected noise distribution.
 2. The method according to claim 1,wherein the step of detecting the edge comprises determining that thereis no edge in the image if an intensity difference between adjacentpixels of the image falls within intensity allowance, and determiningthat there is any edge in the image if the intensity difference betweenadjacent. pixels of the image does not fall within the intensityallowance.
 3. The method according to claim 1, wherein the noiseparameters are Skellam parameters detected from patches having uniformcolor in the image using an ergodic characteristic of a Skellamdistribution of the image.
 4. The method according to claim 1, whereinthe noise parameters are Skellam parameters detected for RGB (Red, Greenand Blue) pixels of the image based on linearity between the noiseparameters of the image and the intensity of the image.
 5. The methodaccording to claim 1, wherein the noise parameters are Skellamparameters detected for RGB (Red, Green and Blue) pixels of the imagebased on a detected relationship between the noise parameters of theimage and the intensity of the image.
 6. A method of detecting an edgeof an image, comprising the steps of: detecting a noise distribution ofan object image; and detecting an edge of the image based on thedetected noise distribution, wherein a degree of edge (e(i,j)) for onepixel of the image is calculated according to the following equations,${e\left( {i,j} \right)} = \left\{ {{{\begin{matrix}{0,} & {{if}\mspace{14mu}\left\{ {\begin{matrix}{{e_{x}^{c}\left( {i,j} \right)} < 0} \\{{e_{y}^{c}\left( {i,j} \right)} < 0}\end{matrix}\mspace{11mu}{for}\mspace{14mu}{all}\mspace{14mu} c} \right.} \\{{{\sum\limits_{c}{e_{x}^{c}\left( {i,j} \right)}} + {\sum\limits_{c}{e_{y}^{c}\left( {i,j} \right)}}},} & {{otherwise},}\end{matrix}{e_{x}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {{i - 1},j} \right)} - {x^{c}\left( {{i + 1},j} \right)}}} - I_{A}}{I_{A}}},{{{and}{e_{y}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {i,{j - 1}} \right)} - {x^{c}\left( {i,{j + 1}} \right)}}} - I_{A}}{I_{A}}}} \right.$where, I_(A) means intensity allowance in a pixel of the image, c meansRGB (Red, Green and Blue) color channels in a color space, and x(i,j)means a pixel value at a position (i,j) of the image.
 7. Anon-transitory computer readable medium recorded with a program forperforming the method according to claim
 1. 8. An apparatus fordetecting an edge of an image, comprising: a noise detecting unit thatdetects a noise distribution of an object image by estimating the noisedistribution according to correlation between noise parameters of theimage and intensity of the image, the noise parameters being Skellamparameters detected for TGB (Red, Green and Blue) pixels of the imagebased on a detected relationship between the noise parameters of theimage and the intensity of the image; and an edge detecting unit thatdetects an edge of the image based on the detected noise distribution.9. The apparatus according to claim 8, wherein the edge detecting unitdetermines that there is no edge in the image if an intensity differencebetween adjacent pixels of the image falls within intensity allowance,and determines that there is any edge in the image if the intensitydifference between adjacent pixels of the image does not fall within theintensity allowance.
 10. An apparatus for detecting an edge of an image,comprising: a noise detecting unit that detects a noise distribution ofan object image by estimating the noise distribution according tocorrelation between noise parameters of the image and intensity of theimage, the noise parameters being Skellam parameters detected from pairsof Skellam parameters and intensity of a set of same pixels having thesame intensity of two static images; and an edge detecting unit thatdetects an edge of the image based on the detected noise distribution.11. An apparatus for detecting an edge of an image, comprising: a noisedetecting unit that detects a noise distribution of an object image, thenoise detecting unit estimating the noise distribution according tocorrelation between noise parameters of the image and intensity of theimage, to the noise parameters being Skellam parameters detected frompatches having uniform color in the image using an ergodiccharacteristic of a Skellam distribution of the image; and an edgedetecting unit that detects an edge of the image based on the detectednoise distribution.
 12. An apparatus for detecting an edge of an image,comprising: a noise detecting unit that detects a noise distribution ofan object image, the noise detecting unit estimating the noisedistribution according to correlation between noise parameters of theimage and intensity of the image, the noise parameters being Skellamparameters detected for RGB (Red, Green and Blue) pixels of the imagebased on linearity between the noise parameters of the image and theintensity of the image; and an edge detecting unit that detects an edgeof the image based on the detected noise distribution.
 13. An apparatusfor detecting an edge of an image, comprising: a noise detecting unitthat detects a noise distribution of an object image; and an edgedetecting unit that detects an edge of the image based on the detectednoise distribution; wherein a degree of edge (e(i,j)) for one pixel ofthe image is calculated according to the following equations,${e\left( {i,j} \right)} = \left\{ {{{\begin{matrix}{0,} & {{if}\mspace{14mu}\left\{ {\begin{matrix}{{e_{x}^{c}\left( {i,j} \right)} < 0} \\{{e_{y}^{c}\left( {i,j} \right)} < 0}\end{matrix}\mspace{11mu}{for}\mspace{14mu}{all}\mspace{14mu} c} \right.} \\{{{\sum\limits_{c}{e_{x}^{c}\left( {i,j} \right)}} + {\sum\limits_{c}{e_{y}^{c}\left( {i,j} \right)}}},} & {{otherwise},}\end{matrix}{e_{x}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {{i - 1},j} \right)} - {x^{c}\left( {{i + 1},j} \right)}}} - I_{A}}{I_{A}}},{{{and}{e_{y}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {i,{j - 1}} \right)} - {x^{c}\left( {i,{j + 1}} \right)}}} - I_{A}}{I_{A}}}} \right.$where, I_(A) means intensity allowance in a pixel of the image, c meansRGB (Red, Green and Blue) color channels in a color space, and x(i,j)means a pixel value at a position (i,j) of the image.
 14. The apparatusfor detecting an edge of an image, comprising: a noise detecting unitthat detects a noise distribution according to a linear relationshipbetween Skellam parameters and intensity of an object image, the Skellamparameters being detected from patches having uniform color in theobject image using an ergodic characteristic of a Skellam distributionof the image, based on the mean and the standard deviation of theSkellam distribution of the image; and an edge detecting unit thatdetects the edge of the image by determining that there is no edge inthe image if an intensity difference between adjacent pixels of theimage falls within intensity allowance and determining that there is anyedge in the image if the intensity difference between adjacent pixels ofthe image does not fall within the intensity allowance, based on thedetected noise distribution, wherein a degree of edge (e(i,j)) for onepixel of the image is calculated according to the following equations,${e\left( {i,j} \right)} = \left\{ {{{\begin{matrix}{0,} & {{if}\mspace{14mu}\left\{ {\begin{matrix}{{e_{x}^{c}\left( {i,j} \right)} < 0} \\{{e_{y}^{c}\left( {i,j} \right)} < 0}\end{matrix}\mspace{11mu}{for}\mspace{14mu}{all}\mspace{14mu} c} \right.} \\{{{\sum\limits_{c}{e_{x}^{c}\left( {i,j} \right)}} + {\sum\limits_{c}{e_{y}^{c}\left( {i,j} \right)}}},} & {{otherwise},}\end{matrix}{e_{x}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {{i - 1},j} \right)} - {x^{c}\left( {{i + 1},j} \right)}}} - I_{A}}{I_{A}}},{{{and}{e_{y}^{c}\left( {i,j} \right)}} = \frac{{{{x^{c}\left( {i,{j - 1}} \right)} - {x^{c}\left( {i,{j + 1}} \right)}}} - I_{A}}{I_{A}}}} \right.$where, I_(A) means intensity allowance in a pixel of the image, c meansRGB (Red, Green and Blue) color channels in a color space, and x(i,j)means a pixel value at a position (i,j) of the image.